Appendix.

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EXAMINATION PAPERS.

1861-1862.

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M A T R I C U L A T I O N E X A M I N A T I O N .

GREEK.

(PROFESSOR IRVINO.)

O. T., ISGl.

ARNOLD, Greek Prose Composition. EURIPIDES,Hecuba;

or XENOPHON, Anabasis, iv., v., vi.

[N.B. The principal parts of a verb are its present, future, and perfect active, perfect passive, .and second aorist active ; or, if deponent, its present middle, future middle, and whatever perfect and aorist it employs. In parsing a verb, give its tense, mood, voice, and principal parts. In parsing a substantive or an adjective, give its gender, number, case, and nominative and genitive singular.]

1. Decline these words? Svopa, was, 58e, yXuKvs, nOeis.

2. Give the principal parts of aklo-Kopxu, fmv$a.v<a,

6vrjaKU>, <f>epuy, TTIVUI, pijYwp.1.

3. Form the 3rd sing. plup. ind. pass, of <j>iKi<o, thc 2nd plur. 1 aor. imper. mid. of fiovXevoi, the 2 aor.

part. act. dat. plur. fem. of ri&ijiu, the 2nd dual perf, ind. pass, of <pa!v<a. •

a 2

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IV EXAMINATION PAPERS,

4. H o w ' d o you represent i n Greek t h o English indefinite article 1

5. To w h a t English pronouns do ovros, eKtii/os, avros, respectively correspond 1

C. " I have a pain i n my head." " Remember what is honorable." " I ceased f r o m work." " I marclicd twenty stadia a d a y . " I n w h a t cases would you p u t in Greek t h e words italicised %

1. P u t i n t o Greek " More wise (o-d$os) t h a n g o o d "

(d-yaflos). " Greater t h a n ever t h e y were."

" Another a r m y in addition to t h e one h e had."

" I t is right t h a t I should do this."

8. Give t h e E n g l i s h of arroOv/jcrKeiv into rtvos* eTrai irpds Ttvos- (xvai Trpds Tin- Kara Ti' eis StSao-KaXou TTtp.ire.LV. ~~

9. Translate literally—

opui a-', ' O o v a c r t v . •

Si//,' eortav T* u<^iifo/xaia

10. W h y is rrpoa-Otyij) conjunctive, not opativc 1 W h y is xp??£ovo-a a participle. W h y is •yevcidSos genitive?

SS>pa accusative %

1 1 . Parse, in t h e above extract, x ^ Pa' ttpoerOiyw, Tr^evyas, \dpt,v, <j>avovp.ai, EXTTIOW, c^ovo-a, l o r t W . 12. W h a t are t h e meanings a n d derivations of KOTO^CS,

V7T07TT0S, •fjKpl/SwKOTC';, Tl/XO)p01J/itVOS, 7t€pt,rtTv^ai, Xpuo"Ot£aijs, t v r i K v o s , {fypovhos.

Or 9. T r a n s l a t e — ' E i m St TO. tTrmySeia

TTI ro\€/XtK(OTClTOVS TU>V «V TO) UoVTlD.

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MATRICULATION. V

10. Why is T/5a-re£ownW genitive? OIKLZV genitive?

pdSiov neuter ? T/yov imperfect ?

11. Parse r/yepovas, kapfldveiv, rjp,iav, eKTromuKoVcs, X<l>pLa, rjyov, iroXeyntKoyrdVovs, iTtaa^ov.

12. What arc the meanings and the derivations of bbontopeiv, dimoToixowres, pLcr6o(popd, TtiXTaarai, avdpurTos, ayopavopos, d^iEios, aipcvSovip-ns'.

F. T., 1S62.

1. Decline these words \ntmv, /Sao-iAeus, Trot^n/s, Tts, iXcvdepos.

2. Give the principal parts of Tthrrw, Ttaid], (p\Xi<o, SiSiopi, TrXrja-cru), opdm.

3. Form the 2nd dual imp. pass, of tlO-npi, the 2nd sing. 1 aor. imper. act of <pcdv<n, the inf. fut. mid.

of npivu), tho 3rd plur. 2nd aor. rjass. of jryyvv/u.

4. By what other name is the 3rd fut. pass, known ? What is the precise force of the tense 1

5. Distinguish the meanings of py voiei, pij Trot^o-^s-

ov p-y'i TTOHyo-fis, oi prq TTOIIJCTI/S.

6. " I had my office taken from me." " I shall over- come my enemies." " I bought the pitcher for sixpence." " H e hit me with a stick." In what cases would you put in Greek the italicised words 1

7. Put into Greek, " Most of the land." "Animals run."

" I think you happy (eu8ai/ton'£o)) in your disposi- tion (rpoVos)." "Would that my sou had conquered in the former battle (p<dxn)-"

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VI EXAMINATION PAPERS, -

8. Give t h e E n g l i s h of irp6s TO $vp.<j>epov £«io-f TO, a v t a Ttdcr)(ui <JOI- £t /XTJ hid crv Se'SoiKa JUT) ov Odvw

irtl T(3 o/xoiot £tvai.

iytii crc KOX dbv iratSa

'A^atois £i 8ta/}X.j6*7/o-o/xat.

10. I n t h e preceding extract w h y is St/catou genitive?

<pav£ti; opativc ? /not dative 1 l a r i indicative a n d n o t optative 1

1 1 . P a r s e i n t h e preceding" extract, SiafSX-nOrja-op-ai, -Kar^avdiTtt, r a ^ w , SoiVai, <paviin, r a v r a , \dpt,v,

I K W t a i / .

12. W h a t are t h e meanings a n d t h e derivations of dcnta(jpa,,avp,TTitvuv,vTtiyyvov, KOTiipu^ES, ^iXoij/v^tLV, oveipocppwv, £7rto"i(£S, ETrtoTijUOS ?

Or 9 . T r a n s l a t e —

'E7rtOTao"0£ Trov, . . . .

. OVSEVI fjfj.!j>v tlmav.

10. I n t h e preceding, w h y is iiriLXovv imperfect 1 wv genitive 1 €tij opative 1 WKTOS genitive ?

11. I n t h e preceding, parse rjv, dyopdo-avT£s, Ka.TapM.$wv, Ip^erat, opfcrt, iyyvraTia, ovScvl, TOVTO.

12. Give t h c meanings .and t h e derivations of Xo^a-yds,

^EuyijXttTEti', TratojvtXa', TtaytcpaTLov, av6r]pep6v, Trfptppifjjvat, ly^ipCBioi', VEoSapros.

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MATRICULATION. Vll

LATIN.

(PROFESSOR IRVING.)

0. T., 1861.

ARNOLD, Latin Prose Composition. VIRGIL, /Eneid II.; or CICERO, de Senectuto and Letters.

[N.B. In parsing a verb, give its tense, mood, voice, arid principal parts. • In parsing a noun or an adjective, its nominative and genitive, gender, number, and case.]

1. Decline throughout magister, dux, velox, mare, iste, qui.

2. Give the principal parts of scdeo, facesso, pono, praebeo, ago, incedo.

3. Distinguish generally the pronouns, is, iste, ille, hie.

4. -" I hope I shall go." " I order you to go." " I ad- vise you to remain." "T ask a few things of you."

" Thc middle of the way." " I will give you the land to dwell in." Give the Latin for these expressions.

5. What are the three senses in which " si quid haberet daret" is employed?

6. I n translating the following, what difference of idiom is to be observed—(1.) Very many of which tilings.

(2.) I fear that he will come. (3.) The Queen has now reigned 24 years. 1(4.) All the wisest phi- losophers. (5.) You would have said. (6.) A pen to write with. (7.) From the destruction of

"Carthage 1

7. What is the construction employed after sequitur, licet, cupidus, accusare, convenirc, vendere 1

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VU1 EXAMINATION PAPERS,

8. Put the following into oratio obliqua introduced by . Dicit—" Ego ctsi pauca habeo, largitor semper fui, t u contra, divitiis onustus, avari partes semper cgisti; quapropter omnes, qui nobiscum versantur, me diligunt tc oderunt."

Assenscrc omnes .

. . . . , non digua fereutis.

1 10. Parse eripui, dedissent, rcposcent, miserere, fruges, vittre, natos, morte.

11. Why is parari infinitive? lacu ablative? restct subjunctive ? animi genitive 1

12. Give the meaning and the derivation of injuria, ambages, conjux, armiger, concretos, compages, tridens, excidium.

Or 9. Translate literally—

Ita enim senectus honesta est

commemoro vespcri.

10. Parse mancipata est, poterit, utor, audierim, au- guruin, monumenta, litteris, cxercenda?.

11. Why is litteris ablative ? audierim subjunctive ? memori-B genitive ? vesperi ablative ?

12. Give thc meaning and the derivation of coacesco, demetendus, refrigeratio, caducus, principium, offensio, tessera, ropudiatus.

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F. T., 1S62.

1. Decline throughout—major, illc, alius,.fclix, res, cor.

2. Give tho principal parts of domo, dico, sperno, jubeo, faveo, penclo.

3. Which are the historic tenses in Latin 1 What tenses of the subjunctive do-they take after them' in dependent sentences ?

4. " H e has informed me of his plan." " H e h a s a d - "

viaed me to come down into the plain." " A man of thc greatest ability." " I gave you my land as a gift." " My name is Gains." " In the lifetime of Augustus." ' Give the Latin for these expressions.

5. Distinguish nolim factum, milium factum: diu, dudum: amare, diligere.

C. In translating the following what differences of idiom are to bo observed—(1.) Lame of one foot. (2.) I remember to have read. (3.) You are envied your success. (4.) Ready to act. (5.) You and I went home. (6.) To take away a man's life. (7.) The City of Melbourne.

7. Put the following into oratio obliqua introduced by Diceb.it:

" Si illis plane orbatus ossein magnum tamen afferret mihi astas ipsa solatium, diutius cnini in hoc desidcrio esse non possum. Omnia autem brevia tolcrabilia esse debent, ctiam si magna sunt.

8. What constructions are employed after Nemo est quin, capax, rcum faccre ahquem, similis, dignus, damnare ?

a 3

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X EXAMINATION PAPERS,

Sic animis juvenum

plurhna mortis imago. • 10. Parse cxegit, domlnata, inertia, limina, victis, relicti,

additus, corpora.

11. Why is faucibus ablative 1 animis dative ? oxx>licet subjunctive? mortem accusative?

12. Give the meanings and the derivations of maostus, ineluctabilis, partus, hastia, surgo, agglomcro, passim, circumtcxtus.

Or 9. Translate literally—

Equidem non video,

. . imitarcntur cum vittc modo atquc constantia.

10. Parse propius, noiniuanda, comxiagibus, denicrsus, sparsissc ccelcstium, La;li, audeam.

11. Wliy is sentiam subjunctive? operc ablative? tue- rentur imperf. subjunctive? corjiora accusative?

12. Give the meanings and thc derivations of uegotinin, cxcusarc, iuipeditus, navigo, rccrudcsco, collega, commendo, oratiuncula.

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ENGLISH.

(PROFESSOR IRVING.) O. T., 1361.

1. What is the real irregularity in thc following plurals which to tho eye appear regular—paths, youths?

2. Mention six English verbs which employ two forms in the preterite tense.

3. " You shall go," " You will go." Explain clearly the difference in meaning between these two forms.

4. What do you.mean by the names Transitive and In- transitive, as applied to verbs? Mention any verb which is used both as Transitive and as Intransitive.

5. When should an adjective follow its noun in Eng- lish 1

G. Correct the following:—

(1.) The conduct of your friend is attempted to lie shewn to have been dishonorable.

(2.) All words which arc signs of conqilex ideas furnish matter of mistake.

(3.) He asked me, who I spoke of.

(4.) Thc child was overlain.

(5.) Immediately consequent to tho victory, Drogheda was invested.

7. Supply the ellipse in—

The book is longer than you thought.

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Xll EXAMINATION PAPERS,

8. " I did not xiass this examination." Tn this sentence in what different positions and with what varia- tions in thc sense can you insert the word "only."

9. What is meant by a solecism? Give examples of this fault.

10. Distinguish — to wave, to waive; to wreck, to wreak; verity, veracity; poem, poetry ; to purpose, to propose; here, hither.

11. How is it,proved that the absolute case in English is thc nominative?

12. " Of two expressions, either of which may be. chosen, that which is strictly nnivocal is to lie X'i'efcrred."

Explain this canon, and give examples of its appli- tion.

F . T., 1S62.

1. What do you mean by the comparative and the su- X>erlative degrees of an adjective, and when is each to be employed.

2. ITosen, shoon are obsolete })lurals. Mention any formed like tlieni which are still used in English.

3. " Ready for choosing." This may have two meanings. State them, and explain the ellipse in each case.

4. When do you call verbs Regular and when Irregular (or weak and strong).

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5. Write out the following, correcting all the errors in spelling—

Their blue threw the sitty fore two dais.a few- rius stawm of unpara-leld violens rendring itt unpleasant to moov owt of doros on a count of the dust and hetc.

G. Correct thc grammatical errors of the following, and give a correct form of each:—

(I.) He caught the words he was not meant to.

(2.) You should have told me, instead of I you.

(3.) The defences are unable to be completed.

(1.) The work what was undertook to be did.

(5.) Tho Georges were the four first kings of the House of Brunswick.

(G.) A soon and prosperous issue.

(7.) The lover got a woman of greater fortune than her he had missed.

7. What is meant by a Barbarism? Give instances of the fault.

8. What were prepositions and conjunctions originally?

9. What gives law to language ?

10. Distinguish—aught, ought; bound, boundeii; kill, murder; intense, intent; justice, justness; poem, poesy.

11. Give thc general rule for the employment of the auxiliaries shall and will.

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XIV EXAMINATION PAPERS,

ARITHMETIC.

(PROFESSOR WILSON.) 0 . T., 1861.

Five questions m u s t be answered correctly to entitle a candidate to pass.

1. Calculate t h c value of a ton of gold at £'3 17s. l O l d . t h e ounce troy. O n e p o u n d avoirdupois contains 7 0 0 0 grains troy.

2. Six inches of wire weigh 37"4 grains ; calculate t h e weight of 100 miles of such wire.

3. I n 400 years there are 97 leap years ; calculate t h e average length of a year.

35 53

4. Express — and —„ as decimal fractions, a d d t h e m together and divide t h e sum b y t h e latter.

5. T h c University enclosure is a square containing forty acres ; how m a n y panels are there in t h c fence, t h c length of each panel being 8 feet 3 inches ? 6. The diameter of t h e earth is 792G miles, and of t h c

moon 2 1 5 3 miles ; t h e distance of t h e moon from t h c e a r t h is 240,000 miles ; supposing t h e e a r t h represented by a globe t h r e e feet in diameter, calculate t o three places of decimals the diameter of a globe which would represent thc moon and t h e distance a t w h i c h i t should b e placed.

7. Shew t h a t any n u m b e r expressed decimally is m u l - tiplied b y 1000 by removing t h e decimal p o i n t three places to t h e right.

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8. Reduce to a single fraction in its lowest terms

3 . J . I + « !»

' 12 l a 27

9. Reduce to its simplest form, I •

n vTi

1 + _{11 13}

10. Find the square root of 14-4 to three places of decimals.

ARITHMETIC.

F. T., 1862.

Five questions must be answered correctly to entitle a candidate to pass.

1. If the dress and arms of a soldier cost £ 5 7s. 5id., what will be the cost of dress and arms for a hundred and twenty thousand five hundred and three men ?

2. What would be the cost of excavating a reservoir three miles long, a mile and a quarter broad, and twenty feet deep, supposing a man to excavate one and a half cubic yards in a day and to receive six shillings for it ?

3. Two clocks are set to the same time ; one of them gains five seconds in two days, the other loses nine seconds a d a y ; after how long will they again mark the same time ?

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XVI EXAMINATION PAPERS,

74 9'

4. Express — and—, as decimals, and divide their

1 10' 104 '

sum by their difference.

5. What will be the cost of digging a ditch round a square piece of land of ninety acres, at half-a-crown for each yard in length of it ?

C. State the rule for simple subtraction. Explain the process called borrowing ten and paying it back again. What is really done in such a case 1 Show- that the result obtained is correct.

7. Reduce to a single fraction in its lowest terms

3 8 7 2

]

L

!) + 3 — 12 + 20 " ' 30 8. Reduce to its simplest form

17 15 21 — 28 2 — — + —

12 42 9. Find the square root of 745'29.

Calculate thc value of ~ of 29 l o places of decimals of a pound.

29

10. Calculate thc value of ~ of £ 5 3s. 6d. to four l o

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^ ?

MATRICULATION. XVU

ALGEBRA.

(PROFESSOR WILSON.) 0. T., 1861.

1. Explain the meaning of (a — b) c + d a — b xc-\-d 2 ( a + b f 2 a + b - and calculate their values when « = 24 6 = 4 c = 5 d - 2 2. Shew that asa7= au

3. Reduce to its simplest form

(ar + y"' + x + y - x y + 1) (.s + y - 1 ) 4. Divide 32a4 + 54«63 - 8164 by 2« + 36

5. Reduce to a single fraction in its simplest form 3a—46 2a — 6 — c 1 5 a - 4 c a—46

~ 7 3 + 12 2 1 ~

6. Reduce to its simplest form

7. Find x from the equation

5 a - 1 9 . r - 7 9 . r - 6 „

— - —

⁺

- i r =

⁰

x= 3 x - - ( i - X -r -

• Z o

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xviii EXAMINATION PAPERS,

9. A travelled x miles in y hours; B travelled p miles in q hours; if A had travelled one mile an hour faster he would have travelled twice as fast as B : find the equation which expresses this final statement.

10. One rod is m times as long as another, and the difference between them is n times the shorter rod;

find the equation between in and n.

F. T., 1862.

1. Explain the meaning of a x b — c, a x ( b — c), a — b x c — d, ah2, (2a6)s and calculate their values when a = 20, 6 = 5 , c = 3, and d = 2.

2. Multiply together «3— a and 3a — a \ 3. Divide 21 x3 + 8y3 by 3x + 2y.

4. Reduce to its simplest form (

*

²

- *

^{+ 1 )}

[ p

⁺

i

^{+ 1}

]

5. Reduce to its simplest form ax — x1 x*

(a + x f ' a2 - x1

6. Reduce to a single fraction in its simjilest form a h Sab

a ^ l ~ a + b

+

b{a

9

-b

1

)

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2 z + 3 - ^ J ? = 7 ( « - l l ) 8. Find x from the equation

x - 2 2 « - 3 S.e-4 5x~G + - = —=—

9. A is x years older than B, and B is y years old. Ten years ago A was twice as old as B. Find the equation between x and y.

10. An iceberg is floating. — of it is above water and -

m n of it under water. Find the equation between m

and n.

GEOMETRY.

Three propositions from the First Book and two from the Second Book must be written out correctly to entitle a Candidate to pass.

Credit will not be given for any proposition in which algebraical symbols are used.

1. From a given point draw a straight line equal to a given straight line.

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XX EXAMINATION PAPERS,

2. If from the ends of one side of a triangle there be drawn two straight lines to a point within the triangle these shall be together less than the other two sides of thc triangle but shall contain a greater angle.

3. If a straight lino fall upon two parallel straight lines it makes the alternate angles equal to one another.

4. Equal triangles upon the same base and upon the same side of it are between the same parallels.

5. The complements of parallelograms which are about the diameter of any parallelogram are equal to one another.

G. On a given straight line describe a parallelogram which shall be equal to a given triangle and have one angle equal to a given angle.

7. If there be two straight lines one of which is divided into any number of parts the rectangle contained by the two straight lines is equal to the sum of the rectangles contained by the undivided line and the several parts of the divided line.

8. Divide a given straight line into two parts so that thc rectangle contained by tho whole and one of thc parts shall be equal to the square of tho other part.

9. In every triangle thc square of thc side subtending cither of the acute angles is less than the squares of the sides containing that angle by twice the rectangle contained by cither of these sides and thc straight line intercepted between the perpendicular let fall upon it from the opposite angle and the acute angle.

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10. Describe a square that shall be equal to a given triangle.

F. T.,1862.

Three propositions from the First Book and two from the Second Book must be written out correctly to entitle a Candidate to pass.

Credit will not be given for any proposition in which algebraical symbols arc used.

1. If two angles of a triangle are equal to one another the sides also which are opposite to the equal angles shall be equal to one another.

2. Shew how to bisect a given rectilineal angle.

3. If at a point in a straight line two other straight lines upon the opposite sides of it make tho adjacent angles together equal to two right angles these two straight lines shall be in one and thc same straight line.

4. If a side of any triangle be produced the exterior angle shall be equal to the two interior and remote angles and the three interior angles shall be together equal to two right angles.

5. Parallelograms upon the same base and between the same parallels are equal to one another.

6. If thc square described upon one of thc sides of a triangle be equal to the squares described upon thc other two sides of it the angle contained by these two sides shall be a right angle.

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XX11 EXAMINATION PAPERS,

7. If a straight line be divided into any two parts' the rectangles contained by the whole line and the two parts severally arc together equal to the square of the whole line.

8. If a straight line be divided into two equal and also into two unequal rjarts the rectangle contained by the unequal parts together with the square of the line between the points of section is equal to the square of half the line.

9. If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole line and that part together with the square of thc other part.

10. In obtuse angled triangles if a perpendicular be drawn from either of the acute angles to the opposite side produced the square of the side subtending the obtuse angle is greater than the squares of the sides containing that angle by twice the rectangle contained by the side upon which when produced the perpendicular falls and the straight line intercepted without the triangle between the perpendicular and the obtuse angle.

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HISTORY.

(PROFESSOR HEARN.) O. T., 1861.

Candidates may select any two of the following divisions.

I. State the periods at which thc following persons respectively lived, and the principal incidents in the public life of each of them

1. Aristomenes.

2. Harmodius.

3. Aristides.

4. Nicias.

5. Brasidas.

6. Lysander.

II, State the respective dates of the following events, and the principal persons and circumstances connected with each of them

1. The First Secession.

2. The Decemvirate.

3. The Capture of Rome by the Gauls.

4. The creation of the office of Praetor.

5. The Final Equalization of the Patricians and Plebeians.

G. The Final Conquest of Italy.

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XXIV EXAMINATION PAPERS,

I I I . State, with respect to each of the following battles, (a.) its date;

(6.) the situation of the battle field;

(c.) the combatants and the commanders on either side;

(d.) thc causes of the war during which it was fought;

1. Evesham.

2. Halidown Hill.

3. Poitiers.

4. Siege of Orleans.

5. Bosworth.

G. Worcester.

F. T., 1862.

Candidates may select any two of the following divisions.

I. State, with respect to each of the following battles, (a.) its date;

(6.) thc situation of thc battle field;

(c.) the combatants and (where they are known) the commanders on either side;

(d.) the causes of thc war during which itwasfought;

1. Thc Cynurian Plain.

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2. The Siege of Miletus.

3. Plata*.

4. Mycale.

5. (Enophyta.

G. Thc Siege of Platan.

I I . State tho respective dates of the following events, and the principal persons and circumstances'connected with each of them.

1. Thc expulsion of the Kings.

2. The league of the Romans with the Latins and the Hernicans.

3. The legalization of intermarriages between Patricians and Plebeians.

4. Thc disaster of thc Caudine Forks.

5. The offering of the Spolia Opima.

G. The suppression of Illyriau Piracy.

I I I . State the periods at which the following persons respectively lived, and the ruincipal incidents in the public life of each of them;

1. Thomas a'Bccket.

2. Simon de Montfort. • 3. Roger Bigocl.

4. Thomas Cromwell.

5. Sir Walter Raleigh.

6. Admiral Blake

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XXVI EXAMINATION PAPERS,

PHYSICAL GEOGRAPHY.

(PROFESSOR M'COY.) 0 . T., 1861.

1. What are the characters of Continental Islands distinguishing them from any other group ? Give the latitude and longitude of examples of Continental Islands related to North America, South America, the Mediterranean, and Asia..

2. Give approximately the boundaries of the Great Asiatic and European Arctic River-basin, and fix the points at which some of its principal rivers reach the ocean.

3. Into what oceans do the principal rivers of Europe N. Asia, E. Asia, and S. Africa, respectively run and what great physical feature mainly influences the two principal directions in which the chief rivers of Europe run?

4. What general laws have been ascertained relating to the direction, rate, origin, and variation of the Cy- clones or Hurricanes of the Antilles, thc China Sea, and the Indian Ocean ?

5. Trace the principal flexures of the lines limiting tho regions in which snow falls at the sea level in both hemisxiheres, giving reasons for thc North and South deviations.

G. Give the boundaries of thc zone of Periodical Rains, with the causes of their chief irregularities, and explain how the rainy and dry seasons of India follow from exceptional causes, other than those regulating the same seasons elsewhere.

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(PROFESSOR M'COY.) F. T., 1802.

1. To what level do glaciers descend on the North and South sides of tho Himalaya respectively, and to what causes is the difference attributable ?

2. What are the electrical peculiarities of thc atmosphere in Thibet, from what conditions of the air do they follow, and what are the physical features which cause those effects ?

3. What neutral points in the sky do not polarise the light of the sun ?

4. Where arc the magnetic poles of the earth?

5. How many points of maximum magnetic intensity exist on the earth's surface, and where are they ? 6. Mention the more remarkable places near which the

Isothermal line of 72° passes in J u l y ; and which Isothermal most nearly coincides with the Trojiic of Cancer in January ?

7. Mention some coasts at which the tide-wave producing high water at twelve o'clock in Tasmania would produce high water at the same hour next night and at the same hour next day.

8. At about what rate does the tide-wave travel in the Atlantic and the Southern Ocean ?

i). Describe the position, extent, elevation, drainage, and other physical characters of the more important parts of the mountain system of Hindostan.

10. State approximately the elevation, size, and position of the principal lakes drained by the St. Lawrence.

b 2

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XXViii EXAMINATION PAPERS,

EXAMINATION FOR EXHIBITIONS AT MATRI- CULATION.—FEBRUARY TERM, 1SG2.

GREEK.

(PROFESSOR IRVING.)

ARNOLD, Greek Prose Composition. EURIPIDES, Hecuba.

XENOPDON, Anabasis, iv., v., vi.

1. Translate carefully—

Aia.Ttopovp.tvij) 8E avT(3

. jLt'>?T£) £' atpotKro, u.TtoSi)(tcrOai.

7) rioXXaSos iv TTOXEI

; . . dXXtt£ao-' "AtSa OaXdpovs.

3. Give the meanings and the derivations of dvairv£So-at, Iva-yKuXSiTES, ei'dip-ordp^iis, to-o^€tXijs, VEOixdpos, tvrptTtr]';, 0£oTrt(pSds, dprt/xa&js.

4. Point out, explain, and illustrate the rjeculiarity of form i n EtXr^a, TttpLppvrjvai, TtpocrayayiLv, Oavovpai, avwopacrra, oipiOptTtrav,

5. Give thc rules of the ordinary Iambic meter of the Hecuba.

G. What is the fundamental notion of the genitive ? Trace it in its various uses after classes of verbs.

7. What arc the xieculiar idiomatic .uses of Xav9dvo>,

</>0aVtD, OVSEI'S OOTTIS, SEI^, avroSt

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MATRICULATION :—EXHIBITIONS. xxix

8. Put into Greek the following sentences—

(1.) I t being no longer permitted us to choose whether wo will have peace or war, we must-take-in-hand the war with all the strength that we have.

(2.) He said that whosoever should transgress the laws which the citizens had enacted, whether small or great, should be punished to death.

(3.) Know that being selfish is the greatest evil.

(4.) All who come from their native land to a colony (dTrotKta), come on thc condition that they are to be on-an-equal-footing with those who have come before.

(5.) Repenting things ill done, and acting rightly, is better by far than sitting down and weejjing.

(G.) One might conjecture from thc blood on the road, beside thc dead man that the murderer himself had had a narrow escape from death.

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XXX EXAMINATION PAPERS,

L A T I N . •;- (PROFESSOR IRVING.)

ARNOLD, Latin Prose Composition. VIRGIL, /Eneid, I & I I . CICERO, de Senectute and Letters.

TULLIUS ET CICERO ET QQ. S. P. D. TIRONI HUMANISS. ET OPT.

1. Vide, quanta sit in to suavitas

. . . Leucade proficiscons, vn. Idus Novembr.

His ego nee metas rerum . . . . . . . fremet horridus ore cmento.

3. Translate into Latin—

Since the matter stands thus, there can be hardly any doubt that these two states, which have already contended a long time for empire, will soon ratify a treaty. And it is to be hoped that this will be a lasting peace, for if neighbouring states were willing to consult their own interests they would sec that by mutually assisting each other, each would grow rich and prosperous.

His debts increase daily: he will soon be insolvent, and will be deprived of his paternal estate; nor does he deserve to be pitied by us, for he has made a bad use of everything, wealth, nobility, and power.

I do not care a straw for your opinion. I have determined to get a contract for building a house, much larger and more splendid than that which I now inhabit. I hope that it will not cost me more than ten thousand pounds.

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MATRICULATION :—EXHIBITIONS. XXxi Derive fully the following words—numen, sator

conticesco, utiuam, claustrum, judex, oblectamenta, villa, insipienter, auctoritas.

ENGLISH.

(PROFESSOR IRVING.) F. T., 1SC2.

[In valuing this paper special regard will be had to the clearness of the writing, and the style as- well as the correctness of the answers.]

1. Write a clear and concise account of—

The expulsion of the Peisistratida?, The overthrow of the second Dccemviratc, Or, The dethronement of Richard I I :

2. Write down six famihar quotations from English . poetry, giving the author and the work from which

each is taken.

3. Trace the following common words to their roots, and show how they have acquired their present meaning—

Gentleman, School, Detest, Engine, Physician, Street.

4. A recent English historian speaks of the lines of Torres Vedras as "works of which the cuttings

" of miles of railroad in a mountainous country

" can furnish but an imperfect idea of their colossal

" x>roportions." Is this sentence incorrect or only awkward ?

Explain your answer and give the sentence iu an amended form. \

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XXX11 .EXAMINATION PAPERS,

5. An English poet has the following—

" all that srjirits pure and ardent

"Arc cast out of love and reverence because chancing not to hold."

What do you take this to mean ? Is the form of expression selected incorrect or only awkward ? G. " Thc question is, were not thc unreflecting multitude

right 1 " Do you consider this construction right or wrong ? Give reasons for your answer.

GEOMETRY.

(PROFESSOR WILSON.)

Credit will not be given for any proposition in which algebraical symbols are used.

.1. Define an angle ; equal angles : a right angle : an acute-angled triangle: an obtuse-angled triangle : parallel straight lines: a parallelogram: a gnomon.

2. Show that the exterior angles made by producing the sides of any polygon are together equal to four right "angles. Is this stated precisely? If not state it precisely.

3. Show that any two angles of a triangle arc together less than two right angles. What is the converse of this proposition ? Show that through thc same point there cannot be drawn two straight hues parallel to the same straight lino.

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4. Show that if Hhe opposite angles of a quadrilateral figure are equal to one another thc figure is a parallelogram.

5. Show that if two triangles have two sides of the ono equal to two sides of the other each to each and an angle opposite to one of these sides in one equal to the angle opposite to the side equal to it in the other and if any one angle of each triangle be a right angle the triangles are equal in all respects.

If it be not given that one angle is a right angle what alternative is admissible ?

C. Show how to a given straight line to apply a rectangle equal to a given rectilineal figure.

7. If from the vertex-of a triangle a straight line be drawn perpendicular to the base thc difference of the squares on thc sides of thc triangle is equal to the difference of the squares on the segments of the base.

8. Show that the perpendicular is the shortest line which can be drawn from any point to a straight line and that of all other lines which can be so drawn one nearer to the perpendicular is shorter than one more remote.

9. Show that the squares described on the diagonals of any parallelogram are equal to the squares on the four sides.

b 3

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XXXIV EXAMINATION PAPERS,

ALGEBRA.

(PROFESSOR WILSON.)

1. Explain and distinguish the words—sum, product, quotient, term, factor, root, index, power, as used in Algebra.

2. Show in what cases a + y is a factor of xn + yn. 3. If a is divided by 6 with remainder c show that all

- the common factors of 6 and c are identical with those of a and 6.

4. If s = h{a + b + c) show that

' a2+b"—c- "I 2 4.s(s — «) (s - V) (s — c) Ca-+b-—c-1 *_<

I 2«6 J " '

^a-b-

5. Show that the same number cannot be added to the numerator and the denominator of a fraction or subtracted from them without altering the value of the fraction except in the case when the fraction is originally unity.

C. Reduce to its simplest form 2a3—3irx+7ax2—3x3

7. Show how to find thc vulgar fraction equivalent to a recurring decimal.

7 3 8 _ 24 8 2 i r 5 x⁺3 x " U x ~ i 5

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9. Find x and y from thc equation 0-3« + 7-05y = 23001 ' -v 1

a -0004 10. Find at what times between ten and eleven the two

hands of a clock will be at right angles to one another.

11, Show that the difference of the squares of any two consecutive numbers is equal to the sum of the two numbers.

HISTORY.

(PROFESSOR- HEARN.) F . T., 1862.

I . — 1 . What circumstances led to the expulsion of tho Alcma!onid£e from Athens ?

2. («.) Describe the political condition of Attica at the time of Solon's legislation.

(6.) What was the distinguishing feature of Solon's Constitution 1

(c.) What new body did he call into existence ? . 3, {a.) Explain thc object of the institution known as

Ostracism.

(6.) To whom is it generally ascribed ?

(c.) On what grounds has it been contended that this institution was practically beneficial ?

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XXXVI EXAMINATION PAPERS,

4. What important change did the Persian invasion produce in the relations of the Greek cities ?

5. (a.) What were the causes of tho war between ^Egina and Athens ?

(6.) How was that war important ?

(c.) Who were the leading citizens of Athens at that time?

6. («.) What was the first occasion in which Cleon appears prominently in Athenian public affairs ?

(6.) Give some account of this transaction.

(e.) Mention some of Cleou's immediate predecessors as popular leaders.

I I . — 1 . (a.) What is the intrinsic value, if any, of the legendary traditions of the Roman people ? (6.) What historical facts, if any, as to the state of

Regal Rome are connected with these traditions ?

2. (a.) When and in what circumstances was the Censorshirj established ?

(6.) Describe the duties of the Censors.

3. Explain the position in which the Roman Govern- ment stood at the conclusion of the first Samnite war—

(a.) To the Army.

(6.) To the Plebeians.

(e.) To the people of Latium.

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4. (a.) When did the epithet "poor" cease to be appli- cable to the Plebeians as a class ?

(6.) State tho principal causes of this change in the condition of the Plebeians.

5. (a.) In what did the burthens of thc Municipal Towns "consist ?

(6.) In what their privileges ?

6. (a.) How did the Colonies secure the supremacy of Rome in Italy ?

(6.) What were the rights and privileges of the Latin Colonies ?

I I I . — 1 . When was the legal equality of all English freemen below the rank of the peerage completely established ?

2. At what time and in what circumstances did the friendly relations which for many years subsisted between France and Scotland arise 1

3. At what time and in what circumstances did Elizabeth accept the protectorate of the Netherlands ?

4. When and on what pretence was the order of Baronetcy created ?

5. Give some account of thc "decimation" of the Royalists by Cromwell, and of the means by which this measure was carried into effect.

6. In the times of the Stuarts what means, if any, existed for the expression of public opinion ?

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XXXVU1 EXAMINATION PAPERS,

PHYSICAL GEOGRAPHY.

(PROFESSOR M'COY.)

1. State distinctly thc two different senses in which the term " magnetic poles" of the earth is used by writers on terrestrial magnetism; as, for instance, by Gauss and by Hallcy.

2. Name, and briefly define, the three elements used in the construction of magnetic charts.

3. State the reasons which you think may account for each of the marked differences between the North- ern and Southern boundaries of the zone of periodic rains.

4. Why do the dry and rainy seasons of India not follow the ordinary rule as to the position of the sun of other places in the zone of periodic rains ? State the times of the succession of the rainy and the dry seasons in the principal districts of India, com- mencing with the vernal equinox.

5. Explain what is understood by the " thermic anom- aly" of Dove, and give some examines of "thermic isabnormals," and show that they may in some cases coincide with isothermals.

G, What are the general conditions influencing the formation of salt lakes in various parts of the world ?

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FIRST- ORDINARY EXAMINATION.

FIRST ORDINARY EXAMINATION FOR T H E DEGREES OF B.A. AND L.L.B.

GREEK.

(PROFESSOR IRVING.) 0 . T., 1861.

DEMOSTHENES, Olynthiac Orations. HOMER, Iliad, Books i.—iv.

[N.B.—In parsing a verb give its tense, mood, and voice; its present, future, perfect, and second aorist active, and perfect passive, if these tenses arc in use ; if not, then thc present, future, and perfect employed by it.]

(a.) 'EtTtl TtoXXZv p.iv dv Tts IStiv,

• crvppd^wv Tt /cat naipS>v.

Or (h.) Oixj, Tavru, Trapt'oTarat poi .

TtoiticrOaL Xdyi 2. Translate literally—

(a.) Trjv 8e piy d^^i;o-as . . . . . TO yap Xd\op.tv yEpas yptis.

Or (6.) uXX' OTE 8i; Tpditacnv . • . . . d'yawd/xtO' «T8os iSovTfS,

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xl EXAMINATION PAPERS,-

3. Draw an outline m a p of Macedonia and Chalcidice, marking t h e position of Olynthus, Pydna, Mcthoue, t h e Pffionians, A m p h i p o l i s ; or of Peloponnesus, marking t h a t of Epidaurus, Pylus, Tegea, Sparta, Mycenae.

4. Parse fully t h e following verbs, i<TKtp,pivo<s, Ttt^yjvivai, t^tracrdycrtTat, Ka6v<j>tipt6a, tuoptOa. : TttitoiOrjS, Ttrp-q^ti, tKay, ftrjatrai, KaTi6tvT0.

5. W h a t is t h e peculiarity in t h e form of wvl, tvioi, tlveica, Tt6vt<I)S, cKarnfitXiTao, ipi^ipevai, t8pev, t^tiviocra, LTtTtrjes, a«;s.

C. Give t h e meanings and tho derivations of tvtpytTrjpM, o/iopos, (JvyK.tKpotrip.ivoi, ptTaytinadiv, ^tiporoviiv • XEvxiiXEfos, iraXtXXoyos, Epmp.os, c/>wt'£oos, UOTTETOS.

7. W h a t is t h e Digamma? Point o u t any lines of cither extract in q. 2 where it is necessary to t h e meter.

8. Explain from Jelf .the construction in t h c following—

(1.) i w voTara Xwfiqvaio (2.) fjtpiy 8' avifirj

(3.) i)p.tTtpai T dXo^ot Kat vr'ptio. riKva

£tar iiti p.tydpovs TtOTihiypcvai (4.) rov Opr/iKa Ttavcrav dotSrjs (5.) a'tO ocpsXss ayap-os T' tptvat

( 6 . ) i K T t p t T t t i v TtoXXoLCTL KO.I I^O^OV r)pll>t(TffLV

(7.) jLt0-Xr?s Kavartiprjs avTifSoXycrai (8.) <bs 8' OTE f^tlpappoL TtorapoC <rvp.pdXXtTov vSoip (9.) iv' ot aXXot tvrv\!i)cn TO vpirtp' dvrjXiiTKtTt (10.) ipuiv ETTtraTTEti' a7ro8oio-£T£

(11.) £uSatju,oo"tv l^cortv vplv yiyvto-Qai

(12.) tirpenZiOvo' mavKaXXicTT' avTWTU.Ttpdyp.a.T t^pi.

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FIRST ORDINARY EXAMINATION. xli

F. T., 1862.

0 6 /JLTJV ov8' tKtivo y ipuM

ih\v dp0uls 7rot?;rf.

Ot 8E 6to\ Trap Ttfjvi.

T&Xivrjv Msi'E'Xaos dyovto.

2 . Draw a m a p of t h e coasts of t h c ^Ggcan, m a r k i n g Troy, Amphipolis, Athens, Lemnos, Crete.

3. Parse fully t h e following TtpocrnvSa, £yy£ydao-ti', iixpv, EO-raoTES, Tapd£n : iyi'WKores, £t]p.LwOrjvaL, Ttapo£vvti, dvyXdiKapev, dTtaXXayivrts.

4 . W h a t is t h e peculiarity iu t h e form of hwya-tai, yovvdcrop.ai, cHjs, iprrrvcracrKe, dyKvXop,7jr£o), iorpaTooiVTO • ^pyddai, r)l3ovX6pt9a, TtaptwaOai, a>L ? 5 . Give t h e meanings and t h e derivations of x@l£"->

TtpofiXrp-L, dyrjpwv, rpi)(9d, Ttrrye.VLp.dXXw : dftOTTtoros, tpiXoTtpaypoavvi], Bavp.aroTtOLwv, acrp;a, cr^sSdi'.

C. Point out a n y lines in t h e second extract in which t h e digamma is necessary, and explain w h y it is so.

7. Explain from Jelf t h e construction iu t h e following—

(1.) TXtaTOpirj vrjt.

(2.) EXEEIVU rtrpLywra'S.

(3.) I ^ s a dyaXXopiEfat.

(4.) p.v$ov aKoi'o-as.

(5.) «)S yvS> ^wo/AEi'oto.

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x l i i EXAMINATION PAPERS, (G.) £tK£r£ x a p p y s 'ApyEtots.

(7.) iyvwKu)¹; « r r a t .

(8.) OVTOIS tir/Orji OOTIS d y v o t t . ( 9 . ) TWV alct)(pwv t e r n . ( 1 0 . ) (TKHTttLfrOl OTtWS p,r) ipovcri, ( 1 1 . ) OVK ULV yvw^XtL rjpHv.

( 1 2 . ) f^tUTW vp!iv ytvitjQai eih'aip.oa-LV.

LATIN.

(PROFESSOR IRVING.) 0. T., 1861.

LIVY, Books IV., V., VI. TERENCE, Adelphi and Andria. MADVIG, Latin Grammar.

(«.) Gcmicius, morte honesta temeritatem luens, . si jirocurata prodigia esscut.

Or (6.) Coniecto in carcerem Manlio

. . linguam et amnios liberaverat homiiium.

(a.) CR. Quid Glycerium ?

dcspoliarc non licet.

Or (6.) Hie suam-sempcr egit vitam

mortem exspectant • scilicet.

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FIRST ORDINARY EXAMINATION. xliii 3. Draw a map of Latium, showing the position of the

Volsci, the iEqui, and the Hernici; and of these towns, Tusculum, Antium, Ardea, Satricum, Alba, Aricia, and of Mount Algidus.

, 4. In what year and by whom was Veil taken ?

5. What was the Rogatio of Canuleius, and in what year was it passed ?

G. Give the meaning and the derivation of colluvio, nuntius, plebiscitum, iunoxius, addictus, sacrilegus, prorsus, patrisso.

7. Give the meaning of receptui cani, malum militibus minari, prajdam publican, apicera dialcm cuilibet imponere, verba alicui dare, lectulos in sole faci- undos dare, quadrupedem constringere, ex ephebis excedere.

8. When are nouns called common ? when epicene ? and when undefined (incerta) ? Give three instances of each class.

9. Give thc meanings of the following nouns in the singular and in the plural—?os, ars, sol, rostrum, hortus, liber.

10. Give the principal parts of stringo, pergo, lavo, tergco, defendo, pungo, lino, repcrio, fateor, paciscor.

11. What are the irregularities in the conjugation of fero, edo, volo ?

12. In the following examples from Livy what would the uses of the oblique cases be styled by Mad- vig 1—

(1.) Hajc omnia celeritate ingenti acta.

(2.) Tribuni militum consular! potestate.

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xliv EXAMINATION PAPERS,

(3.) Rex Veicntum gravis genti fuerat opibus supcrbiaque.

(4.) Momento temporis dcjccti sunt muris.

13. What would be the more correct form of each of the following 1—

(1.) Jovis epulum num. alibi quam in Capito- lio fieri potest ?

(2.) Hand dubium est, quin Chromes tibi non dat gnatam.

(3.) Pcrficietur bcllum si nrgemus obsessos.

(4.) Locum quern communircnt capiunt.

14. What view is taken of an action when it is described in the imperfect, the pluperfect, the futurum exactum ?

F. T., 1862.

Nempe hoc sic esse opinor

interea aliquid accident boni.

Tribunorum plcbis actioncs . . . . ; Romam pcrfugere.

2. Give the geographical position of Vcii, Andros, Clusium, Verona.

3. What account does Livy give of the coming of the Gauls into Italy ?

4. Give a brief sketch of the history of Camillus.

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FIRST ORDINARY EXAMINATION. x l v

5. Give the meanings and the derivations of tibicina, dirimo, discrimen, collega, venustus, prudcns, obsecro, psaltria.

C. Explain lupus in fabula, tegula publice prcebita est, fratri sedes fient perviob, vidi Cantharam suffarcina- tam, paucis te volo, jura gentium, domi militiroquc, oera multibus constituta.

7. What classes of words in Latin are, without reference to the termination, known to be neuter ?

8. Mention six nouns used in the plural only, with their meanings. .

9. Give the principal parts of veto, censeo, soleo, cingo, mcto, nosco, fugio, sapio,reor, texo.

10. What is' meant by an impersonal verb ? Mention four.

1 1 . Mention six adjectives which have assumed the force of independent substantives. •

12. How are the Latin supines and gerunds employed ? 13. What verbs are commonly omitted in Latin ?

ENGLISH AND LOGIC, PART I.

(PROFESSOR IRVING.) 0 . T., 1861.

1, What does Latham mean by an unstable combination of sounds ? Give two instances.

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Xlvi EXAMINATION PAPERS,

2. Two characters used in the Anglo-Saxon alphabet are lost in English. What are these, and what the sounds represented by them 1 Show that the sounds are to be found in English.

3. Give Latham's rule for the relation borne to each other by the two parts of a true compound. Cite four examples in sux>port of the rule, and two apparent exceptions.

4. What classes of derivations are formed by thc following suffixes : -er, -en, -ing, -ock ? Give examples;

5. Decline throughout thc Anglo-Saxon pronoun so, seo, thset, and show what parts of it are retained in English, and how they are emx>loyed.

6. Explain these forms—yclad, worse, did, and the double form in sang and sung.

7. What figures arc exemplified in the following—

(1.) He flung his whole soul into the cause, and his massive form into the saddle.

(2.) If thou thou'st him twice or thrice.

(3.) To bo or not to be, that is the question.

(4.) Set it down in black and white.

8. At what periods, and in what ways, were Latin words brought into use in England 1 Give examples of each period.

9. When did English supplant French—(1.) In school teaching; (2.) In trials; (3.) In statutes?

10. Give Craik's distribution of the Indo-European

• languages, distinguishing the dead from thc living languages.

11. Explain how language abbreviates thinking.

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FIRST ORDINARY EXAMINATION. xlvii 12. Give the contradictory and the converse of the

proposition—Some trees, are fruitbearing, and the subaltern and .every possible converse of All men are lovers of justice.

13. Write down examples of a pair of Relatives, an Abstract noun, a Common noun, a Negative noun.

14. Divide Proposition according to substance, to quality of the Expression and to quantity.

15. Give examples of Definitions obtained in the six ways enumerated by Thomson.

1G. Construct a scheme of classification of not less than four stages. Point out in it (1.) a differentia, (2.) co-ordinate species, (3.) a subaltern genus, (4.) an infima species.

17. Explain thc terms Abstraction and Generalization.

F. T., 1862.

1. What is the account given by Latham of the sounds represented by y, w, ng ?

2. How is quantity estimated in Latin and-in English 1 3. Give and explain Latham's definition of a compound.

4. What kind of adjectives are formed by the termina- tions -y, -ish, -en, -ly ?

5. From what parts of what Anglo-Saxon pronouns is the 3rd personal rirououn now in use formed ? C. Explain these forms—hight, children, last, better.

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xlviii EXAMINATION PAPERS,

7. What figures are exemplified in:— • (1.) For the rain it raineth every day.

(2.) The chaste,- the fair, the unexprcssive She.

(3.) Blue and yellow make green.

(4.) If I am prudent you have not enough.

8. When did the Danes invade England, and in what parts of the island has their language had most influence ?

9. What were the Languc d'Oc and the Langue d'Oyl?, Why so called ? And when was each introduced to England ?

10. Enumerate the living Celtic languages.

11. ' I f man is rational man is responsible.' What kind of proposition is this ? How do Whatcly and Thomson respectively reduce it ?

12. Give a genus, a species, and a property of the term ' House.'

13. Enumerate the various kinds of conversion given by Whately, with examples.

14. 'Language is analytic, Art synthetic' Explain briefly what is meant by this.

15. To what" class of nouns is thc term abstract usually applied ? On what ground may exception be taken to this usage ?

1G. Thc same notion may be spoken of as a Logical and as a Metaphysical whole. Explain this.

17. How arc singular propositions dealt with in Logic, and why ?

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GEOMETRY AND TRIGONOMETRY.

(PROFESSOR WILSON.)

0. T.,1861.

Eight questions must be answered correctly to entitle a candidate to })ass.

Credit will not be given for • any proposition from Euclid in which algebraical symbols are used.

1. Show that if two straight lines be drawn from the ends of one side of a triangle to any point within the triangle these two straight lines will be together less than the other two sides of the triangle but will contain a greater angle.

2. If a straight line be divided into two equal parts .and also into two unequal parts show that the squares of the two unequal parts are together double of the squares of half thc line and the line between the points of section.

3. Show that the straight line drawn at right angles to the diameter of a circle from the extremity of it does not meet the circle iu any other point.

4. Show that thc opposite angles of any quadrilateral figure inscribed in a circle arc together equal to two.

right angles.

5. Show that the angle in a semicircle is a right angle and that the angle in a segment of a circle greater than a semicircle is less than a right angle.

6. Show how to describe an isosceles triangle having each of the angles at the base double of the third angle.

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1 EXAMINATION PAPERS,

7. Show that if thc sides of two triangles about each of their angles arc proportionals thc triangles will bo equiangular and those angles will be equal which are opposite to tho homologous sides.

8. Show that in any right-angled triangle any rectilineal

» figure described on the side opriosite to the right angle is equal to thc sura of two similar rectilineal figures similarly described on thc sides containing the right angle.

9. Show that if- two straight lines which meet one another be parallel to two other straight linos which meet one another and arc not in the same plane with the fust two thc x>la-uc passing through the ono pair is parallel to thc plane passing through the other pair.

10. Show that if two straight lines bo cut by parallel planes they shall be cut in tho same ratio.

11. On a given straight lino as base describe an isosceles triangle having each of the angles at thc base ono quarter of the third angle.

12. The two shorter sides of a right-angled triangle drawn on a horizontal plane are a and 6 and at the angles vertical posts are erected whose heights arc / , g and h ; calculate the lengths of the lines joining their summits.

13. Calculate the angle subtended by a target six feet high at the distance of two hundred yards in degrees minutes and seconds.

14. Define the cosine of an angle and show that it is negative when thc angle is greater than one right angle and less than two.

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lo. Sin •.4=0-0. Calculate cos — and explain why there are two values. -•

IG. A. circle is described whose radius is a quarter of a mile : calculate the distance of the middle point of a chord a hundred feet long from the middle xioint of the corresponding arc.

17. Find an expression for the area of a triangle in terms of any two sides and the included angle.

18. Tho sides of a triangle are 937-5, 842-5 and 788-5 links-; calculate its angles and its area.

19. At what height must the lamp of a lighthouse be placed that it may be just visible forty miles off from the deck of a ship ten feet above the water.

20. Find an expression for the area of a regular polygon of n sides inscribed in a circle whose radius is a : and deduce the area of the circle.

21. Find thc cxjircssion for the radius of a circle circumscribed about a given triangle.

22. Show that the same column of differences will he sufficient for thc Log-secants and the Log-cosines.

F. T., 1802.

Eight questions must be answered correctly to entitle a candidate to pass.

Credit will not be given for any proposition from Eiiclid in which algebraical-symbols arc used.

c 3

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Hi EXAMINATION PAPERS,

1. Show that any two sides of a triangle are together greater than the third side.

2. Show that if a straight line be divided into any two parts thc rectangle contained by the two parts together with the square of one of them is equal to the rectangle contained by the whole and that one.

3. Show that if two straight lines in a circle wluch do not both pass through the centre cut one another they do not bisect one another.

4. Show that equal straight lines iu a circle are equally distant from the centre.

5. Upon a given straight line describe a segment of a circle wliich shall contain an angle equal to a given angle.

G. Inscribe an equilateral and equiangular pentagon in a given circle.

7. Show that if two sides of any triangle be cut proportionally the straight line which joins the points of section will be parallel to the tliird side of the triangle.

8. Show that equiangular parallelograms have to one another thc ratio compounded of the ratios of their sides.

9. Show that if three straight lines meet all in one point and a straight line stands at right angles to each of them in that point these three straight lines shall be in one plane.

10. Show how to draw a straight line perpendicular to a given plane from a given point above it.

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FIRST ORDINARY EXAMINATION. liii 11. Show that if two equal straight lines contain an

angle equal to two-thirds of two right angles the diagonal through that angle of the parallelogram described on them will be equal to either of them.

12. Show that if the surface of a sphere be cut by a X>lane thc section will be a circle.

13. At what distance must a shilling whose diameter is eleven-twelfths of an iuch be x>laced that it may just cover the sun whose angular diameter is 30

minutes ?

14. Define the versed sine of an angle and trace its changes in magnitude as thc angle increases from 0° to 180°.

15. Tan ..-1=0'9. Calculate sin A and tan - . A 2

16. The front of a number of houses built in a crescent is an arc of a circle whose chord is 500 feet and the perpendicular distance of the middle point of the chord from the crescent is 100 feet calculate thc radius of thc circle.

17. Show that in any triangle the sines of the angles are to one another in the same ratios as the sides opposite to them.

18. Two sides of a triangle are 1437 and 2985 links and the angle included by them is 57° find the other angles of thc triangle.

19. At what height must the lamp of a lighthouse be placed that it may be' just visible thirty miles off from thc deck of a ship twelve feet above the water 1

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U v EXAMINATION PAPERS,

20. Find thc length of the side of a regular octagon circumscribed about a circle whose radius is fifteen feet.

21. Explain tho several steps in finding the log. cosine of an angle which lies between two registered in the tables.

22. Calculate J 3 cos 31° 45' 20".

ALGEBRA.

Eight qucstiona must be ansivcred correctly to entitle a candidate to j>ass.

1. Reduce to its simjdest form (•* + ! / ) ' - x~ - f {x + y f - x * - , / 2. Reduce to its simplest form

, f l^f i flz^l f i+ _f_l

L l + y J [ x + x2 J I 1 — x } 3.. Reduce to its simplest form

3 + 2;« 2-3x- 16.r-.rr 2 + x x-—i - + 4. Find thc square root of

a w x- a

•r +-!.+ - + -. — ax - 2 4 x- a- . X

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5. A straight hue is divided into two parts so that thc rectangle contained by the whole line and one of the parts is equal to six times thc square of the other part : find thc ratio of the two parts.

c TC a c , ,, , 2a — 6 2c - d 6. If r = - show that — = -•

b d a — Z b c - 2d 7. Find x from the equation

x x X x 1 3_4+G = 8+i l 8. Find ;>; from thc equation

?_•!:-.,

x 3 "

9. Find x and y from thc equations

3K —5 y „ 2x + y x - 2 i / x II

- 2 -

^{+ 3 =}

~

⁸

- V = 5

⁺

3

10. Thc resistance of a wire to the passage of an electric current varies directly as its length and inversely as the area of its section : the area of a circle varies as the square of its diameter : find how much wire one-hundredth of an inch iu diameter will offer the same resistance as a mile of wire a quarter of an inch iu diameter.

11. A cask contains a mixture of 12 gallons of wine and 18 gallons of water, and another cask contains a mixture of 9 gallons of wine and 3 gallons of water;

how many gallons must be drawn from each so as to produce a mixture containing 7 gallons of wine and 7 gallons of water.

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I v i EXAMINATION PAPERS, '

12. The velocity with which water flows from an orifice varies as thc square root of its depth below the surface, and the quantity which flows out in a given time varies as the area of the orifice and thc velocity jointly ; find what must be the side of a square orifice at the depth of sixteen feet, in order that the same quantity of water may flow from it as from an orifice half an inch deep and two inches broad at a depth of one foot.

• 13. When a body floats in a liquid the volume of thc part immersed varies directly as the specific gravity of the floating body and inversely as that of the liquid : when the specific gravities are equal tho whole solid is immersed : find to what depth a six inch cube of iron whose specific gravity is 7-844 will sink in mercury whose specific gravity is 13568.

] 4. Find an expression for thc number of permutations of n things taken r together.

15. How many different ministries consisting of nine men, two of whom must be lawyers, can be formed out of eighteen members of whom four are lawyers;

no regard being had to political consistency.

16. Investigate an expression for the sum of n terms of a series of quantities iu Arithmetical progression.

17. Find the sum of n + 1 terms of the series x" + xn'hj + xn--yn- + , &c.

18. Show that in the equation on2 —ax + b = 0

a is the sum of the roots and h the product.

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FIRST ORDINARY EXAMINATION. Ivii

F. T., 1802,

Eight questions must be answered correctly to entitle a, candidate to pass.

1. Reduce to a single fraction in its simplest form 5 1 2 4 _ 2 ( . r + l j 1 0 ( . r - l ) 5(2*+3) 2. Reduce to its simplest form

X

—

r

x1 •

- +

V 1

— - y

i

— X

1

+ -

X

3. Find the lowest common multiple of 3x2 - 5 x + 2 and 4x* - ix2 - x + 1.

4. Find the equare root of

i " I i n 6 ix- + l l x + - + 0

a- x

5. A can run six miles while B is running five ; at what point between two stations a mile apart must a post bo placed that A from his end may run to it and back again while B from his end is running to it ? G. Show that when - = - = -; each of these fractions is

b d j a + c+e

equal to -—-—-

1 b + d + f 7. Find x from the equation

0-3 (0-78s - 5-1) - 2-3« (9-7 - 0003) = C-301K.

c 3

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Iviii EXAMINATION PAPERS, 8. Find x from thc equation

(2.K - 3 ) ' = 8,r.

9. Find x and y from tho equations

5-9iK + 7-01y = 21-79 0-007*'= 3-09^.

10. The weight which a rectangular beam will bear without breaking varies directly as its breadth and as the square of its depth and inversely as its length : what must be thc depth of a beam twenty- five feet long wliich will just bear double the weight which another beam half thc breadth sixteen feet long and eight inches deep will bear.

11. When a body floats in a liquid the volume of the jiart immersed varies directly as tho specific gravity of the floating body and inversely as that of thc liquid : when the specific gravities are equal the whole solid is immersed : find to what depth a twelve inch cube of pine whose specific gravity is 0'72 will sink in water whose specific gravity is 1.

12. Find an expression for the number of permutations of n things taken r together.

13. There arc fourtoon subjects which may be taken at the- second ordinary examination in live of which the Candidate must pass : in how many different ways can he select his five subjects ?

14. Find an expression for the limit of thc sum of a scries of quantities decreasing in geometrical progression.

15. Find thc sum of tliirty terms of the series 4 + 1 1 + 1 8 + . . .

1C. Find a vulgar fraction equal to tho recurring decimal 39-3939....

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17. Find the relation between a and 6 that thc two roots of the equation

x2 + ax + 6 = 0 may be equal to one another.

CHEMISTRY AND M1NRKALOCY.

(iMtOFKSSOR M'COY.) 0. T., 1301.

1. What arc thc tests, both in thc dry and wet way, for distinguishing potash from soda ?

2. What are the chief chemical characters of Fluorine ? 3. Give the arguments used in support of the three

different views held by chemists as to thc composition of Silica ?

4. Give tho chief chemical and physical characters of the Mineral Tiucal.

5. In a hexagonal prism of Quartz terminated at each end by a six-sided pyramid what arc the relations of the faces to the lihombohedron ?

C. Define thc tiiclinic or anorthic system of Crystals and mention the most striking peculiarity of form distinguishing such crystals to the eye.

7. Give the characters of C2 I P and show its general relations to the Alcohols and Ethers.

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Ix EXAMINATION PAPERS,

8. What arc the gaseous liquid and solid results of the destructive distillation of Coal ?

9. Describe thc Electrolysis of Oxygen Salts by weak and strong currents respectively.

10. Write a list of the Metalloids in the order of their electro-chemical powers.

11. Define all the fundamental forms of Crystals,

F. T , 1802.

1. What systems of crystals refract light doubly ? 2. If you had to determine by polarized light whether

a transparent slice of a crystalline mineral belonged to the llhombohcdral, thc Cubic or the Pyramidal (or dimctric) system what appearances would you expect in each case ?

3. In pyroelectric prismatic minerals which are the

" analogous " and which the antilogous poles ? 4. Give an example of the formula for ascertaining thc

specific gravity of solids taking any hypothetical or real case and giving the various weights and calculations in full.

5. Mention some of the protoxide isomorphons or plesio- morphous bases replacing Iron in minerals. Give also some of the sesquioxide groux> and state the nature of thc law of Isomorphism or Plcsio- morphism.

C. Mention some examples in the mineral kingdom of Dimorphism and of Trimorphism and explain what is meant by those terms.